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 A160009 Numbers that are the product of distinct Fibonacci numbers. 26
 0, 1, 2, 3, 5, 6, 8, 10, 13, 15, 16, 21, 24, 26, 30, 34, 39, 40, 42, 48, 55, 63, 65, 68, 78, 80, 89, 102, 104, 105, 110, 120, 126, 130, 144, 165, 168, 170, 178, 195, 204, 208, 210, 233, 240, 267, 272, 273, 275, 288, 312, 315, 330, 336, 340, 377, 390, 432, 440, 442, 445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Starts the same as A049862, the product of two distinct Fibonacci numbers. This sequence has an infinite number of consecutive terms that are consecutive numbers (such as 15 and 16) because fib(k)*fib(k+3) and fib(k+1)*fib(k+2) differ by one for all k >= 0. It follows from Carmichael's theorem that if u and v are finite sets of Fibonacci numbers such that (product of all the numbers in u) = (product of all the numbers in v), then u = v. The same holds for many other 2nd order linear recurrence sequences with constant coefficients. In the following guide to related "distinct product sequences", W = Wythoff array, A035513: base sequence distinct-product sequence A000045 (Fibonacci) A160009 A000032 (Lucas, without 2) A274280 A000032 (Lucas, with 2) A274281 A000285 (1,4,5,...) A274282 A022095 (1,5,6,...) A274283 A006355 (2,4,6,...) A274284 A013655 (2,5,7,...) A274285 A022086 (3,6,9,...) A274191 row 2 of W: (4,7,11,...) A274286 row 3 of W: (6,10,16,...) A274287 row 4 of W: (9,15,24,...) A274288 - Clark Kimberling, Jun 17 2016 LINKS T. D. Noe, Table of n, a(n) for n=1..1000 MATHEMATICA s={1}; nn=30; f=Fibonacci[2+Range[nn]]; Do[s=Union[s, Select[s*f[[i]], #<=f[[nn]]&]], {i, nn}]; s=Prepend[s, 0] CROSSREFS A059844, A065108 Sequence in context: A177445 A022826 A053035 * A049862 A022829 A347645 Adjacent sequences: A160006 A160007 A160008 * A160010 A160011 A160012 KEYWORD nonn AUTHOR T. D. Noe, Apr 29 2009 STATUS approved

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Last modified August 9 08:03 EDT 2024. Contains 375034 sequences. (Running on oeis4.)